cosets

Produce cyclotomic cosets for Galois field

Syntax

cst = cosets(m)

Description

cst = cosets(m) produces cyclotomic cosets mod 2^m-1. Each element of the cell array cst is a Galois array that represents one cyclotomic coset.

A cyclotomic coset is a set of elements that share the same minimal polynomial. Together, the cyclotomic cosets mod 2^m-1 form a partition of the group of nonzero elements of GF(2^m). For more details on cyclotomic cosets, see the works listed in References.

Examples

The commands below find and display the cyclotomic cosets for GF(8). As an example of interpreting the results, c{2} indicates that A, A2, and A2 + A share the same minimal polynomial, where A is a primitive element for GF(8).

c = cosets(3);
c{1}'
c{2}'
c{3}'

The output is below.

ans = GF(2^3) array. Primitive polynomial = D^3+D+1 (11 decimal)
 
Array elements = 
 
     1


 
ans = GF(2^3) array. Primitive polynomial = D^3+D+1 (11 decimal)
 
Array elements = 
 
     2     4     6


 
ans = GF(2^3) array. Primitive polynomial = D^3+D+1 (11 decimal)
 
Array elements = 
 
     3     5     7

References

[1] Blahut, Richard E., Theory and Practice of Error Control Codes, Reading, MA, Addison-Wesley, 1983, p. 105.

[2] Lin, Shu, and Daniel J. Costello, Jr., Error Control Coding: Fundamentals and Applications, Englewood Cliffs, NJ, Prentice-Hall, 1983.

See Also

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